Solve [(15div5)^{4}]^{3}:[(2^{2}*5*3):12-2^5:2^4]^10-1^3

$$[ ( 15 \div 5 ) ^ { 4 } ] ^ { 3 } : [ ( 2 ^ { 2 } \times 5 \times 3 ) : 12 - 2 ^ { 5 } : 2 ^ { 4 } ] ^ { 10 } - 1 ^ { 3 }$$

Evaluate

$$8$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\left(\frac{15}{5}\right)^{12}}{\left(\frac{2^{2}\times 5\times 3}{12}-\frac{2^{5}}{2^{4}}\right)^{10}}-1^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\frac{\left(\frac{15}{5}\right)^{12}}{\left(\frac{2^{2}\times 5\times 3}{12}-2^{1}\right)^{10}}-1^{3}$$

Divide 15 by 5 to get 3.

$$\frac{3^{12}}{\left(\frac{2^{2}\times 5\times 3}{12}-2^{1}\right)^{10}}-1^{3}$$

Calculate 3 to the power of 12 and get 531441.

$$\frac{531441}{\left(\frac{2^{2}\times 5\times 3}{12}-2^{1}\right)^{10}}-1^{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{531441}{\left(\frac{4\times 5\times 3}{12}-2^{1}\right)^{10}}-1^{3}$$

Multiply 4 and 5 to get 20.

$$\frac{531441}{\left(\frac{20\times 3}{12}-2^{1}\right)^{10}}-1^{3}$$

Multiply 20 and 3 to get 60.

$$\frac{531441}{\left(\frac{60}{12}-2^{1}\right)^{10}}-1^{3}$$

Divide 60 by 12 to get 5.

$$\frac{531441}{\left(5-2^{1}\right)^{10}}-1^{3}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{531441}{\left(5-2\right)^{10}}-1^{3}$$

Subtract 2 from 5 to get 3.

$$\frac{531441}{3^{10}}-1^{3}$$

Calculate 3 to the power of 10 and get 59049.

$$\frac{531441}{59049}-1^{3}$$

Divide 531441 by 59049 to get 9.

$$9-1^{3}$$

Calculate 1 to the power of 3 and get 1.

$$9-1$$

Subtract 1 from 9 to get 8.

$$8$$

Factor

$$2^{3}$$